Shape from texture: General principle

摘要

The 3D shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed. Our method does not require recognition of the “structure”—regularity, periodicity, parallelism, orthogonality, etc.—of the texture distribution. First, the “homogeneity” of a discrete texture is precisely defined in terms of the “theory of distributions”. Next, distortion of the observed texture due to perspective projection is described in terms of the “first fundamental form” expressed as a function of the image coordinates. Based on this result, the 3D recovery equations for determining the surface shape are derived for both planar and curved surfaces. Some numerical schemes for solving these equations are proposed. Ambiguity in the interpretation of curved surfaces is also analyzed. Finally, some numerical examples for synthetic data are presented, and our method is compared with other existing methods.